"After careful consideration, it was decided that there were no reasonable prospects of success of appeal on errors of law."

A magistrate convicted Wilson earlier this year but District Court judge Roy Ellis in early December ordered the clergyman be discharged.

The judge said there was a reasonable doubt whether Wilson remembered being told about the abuse in 1976 or believed the victim had been preyed upon by pedophile priest James Fletcher.

He said suspicion was not a substitute for proof.

The NSW attorney-general immediately asked the DPP to consider appealing the decision but on Thursday confirmed prosecutors didn't intend to pursue the case further.

"The Office of the Director of Public Prosecutions has informed me this afternoon that it does not intend to commence an appeal from the decision of District Court Judge Ellis to dismiss the charge against former archbishop Philip Wilson," Attorney-General Mark Speakman said in a statement.